A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34,25 Inches (in.), a height of 69,37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping box?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
Other Related Questions
What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Type your answer in the boxes. You may use numbers and/or a negative sign (-) in your answer.
A total of 42 runners dropped out before finishing the race. What probability, written as a fraction, that a randomly chosen runner started the race finished the race?
Correct Answer & Rationale
Correct Answer: 583/625
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
The graph of the equation y = x^2 + 4x - 5 is shown on the grid. Which statement is true when y = 0?
- A. x= -5 and x=1
- B. x= -2
- C. x= -5 and x = 0
- D. x= -9
Correct Answer & Rationale
Correct Answer: A
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Based on the scatter plot, what is the range of ages of the top 10 runners?
- A. 9
- B. 1
- C. 16
- D. 40
Correct Answer & Rationale
Correct Answer: C
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.